AP PreCalc Unit 3 Trigonometric Identities

Pythagorean Theorem

Sin²X + Cos²X = 1

Pythagorean Theorem with Secant

1 + tan²X = sec²X

Pythagorean Theorem with Cosecant

1 + cot²X = Csc²X

Sine

Sinx = 1/cscx

Cosine

Cosx = 1/secx

Tangent

Tanx = 1/cotx

Cosecant

Cscx = 1/sinx

Secant

Secx = 1/cosx

Cotangent

Cotx = 1/tanx

Tangent Identity

Tanx = sinx/cosx

Cotangent identity

Cotx = cosx/sinx

Sine Sum Identity

Sin(α+β) = sinαcosβ + cosαsinβ

Sine Difference Identity

Sin(α-β) = sinαcosβ - cosαsinβ

Cosine Sum Identity

Cos(α+β) = cosαcosβ - sinαsinβ

Cosine Difference Identity

Cos(α-β) = cosαcosβ + sinαsinβ

Sine Double Angle Identity

Sin(2x) = 2sinxcosx

Cosine Double Angle Identity (cos and sine)

Cos(2x) = cos²x-sin²x

Cosine Double Angle Identity (with sine)

Cos(2x) = 1 - 2sin²x

Cosine Double Angle Identity (with cos)

Cos(2x) = 2cos²x - 1